I think, they should be allowed. I see no reason to forbid them. Something, that is easy-too-google for native speaker, may be almost-impossible-to-google for novice learner (IMO, successful googling for things that are underrepresented over the Internet requires the language barrier to be already overcome at certain level).
I think that ideally there should be certain rules on what is not to be asked (not generic "something that is easy to google" — because it's too unclear). For example, dictionary questions (except for when dictionaries doesn't clarify some specific point or there's stable divergence between dictionary form and everyday usage, like here). Sadly, I don't have time to state/propose them now.